A hand-held calculator is an important and useful device. Similar to a computer, the hand-held calculator has a processor, a memory, a display, and an input device; however, there are important distinguishing differences between the hand-held calculator and the computer.
The hand-held calculator is a specialized device and not a general purpose device; as is true of a computer. Because of this specialization, typically the hand-held calculator costs less, has a longer useful lifespan, and is more reliable and more portable than the computer.
Whereas a general purpose computer is capable of executing many different programs, a hand-held calculator typically executes a single program and less frequently supports execution of user-created programs. Normally, a hand-held calculator supports addition, subtraction, multiplication, and division of numbers, either integer-based or decimal-based, entered by a user and displays the results on a built-in display.
A graphical calculator is a further specialized version of a hand-held calculator having a display which is typically larger than a regular hand-held calculator display in order to enable graph output. In many instances, graphical calculator displays are liquid crystal displays for more accurate representation and enhanced readability of a graph output.
A graphical calculator is able to display a graph of a specific expression, e.g. a sine wave representing a sinusoidal function, entered by a user. Disadvantageously, graphical capabilities on hand-held calculators are only available as part of expensive and complex, “high end” scientific calculators. These graphical calculators are more expensive than other calculators, typically costing hundreds of dollars. These graphical calculators are more complicated to operate than other calculators because of the large amount of functionality incorporated therein.
The increased functionality has required a corresponding increase in the number of keys required for manipulating and using the calculator. For example, currently available graphical calculators have approximately fifty (50) keys including two (2) shift or modifier keys for a user to manipulate, e.g. a Texas Instruments (TI) 83 plus calculator has 51 keys and two (2) shift keys which can be used concurrently, enabling up to four functions to be assigned per the 51 remaining keys, and a Hewlett-Packard (HP) 48G+/GX calculator has 49 keys and three (3) shift keys, enabling up to six functions to be assigned per the remaining 49 keys.
Additionally, and in conjunction with the larger number of keys present, a user must contend with different modes of operation of the current graphical calculator. Different modes of operation, accessible via specific keys and/or key sequences, must be utilized in order to access specific calculator functionality, e.g. a graphical calculator may include a fraction mode, a decimal mode, a binary mode, a hexadecimal mode, a finance mode, a statistics mode, and a graph mode.
Further, expression input requires increasingly complicated key manipulations and combinations. For example, in order to graph an expression, there are typically three combinations to be entered: a mode specifying combination, an expression entry combination, and a completion combination. The mode specifying combination may include manipulation of a graph key to instruct the calculator to graph the following expression entry. The expression entry combination may include manipulation of multiple keys to input the expression to be graphed and the completion combination includes manipulation of a key, e.g. an enter key, to instruct the calculator to perform the preceding operations, i.e. graph the entered expression.
Requiring a user to manipulate multiple keys increases the need for learning, the possibility of error and may lead to frustration on the part of the user. Also, requiring additional key presses by a user requires more time and slows the entry and use of the calculator by the user. The addition of multiple modes, complicated expression input combinations, and ever increasing numbers of keys results in a very complicated device.
As further evidence of increasing complexity, the user manual for a currently available hand-held graphical calculator has dramatically increased in size in order to fully explain the use of the calculator. For example, the above-cited TI-83 plus calculator manual includes 269 pages and the HP 48G+/GX calculator manual includes 506 pages. These are very long documents which are typically not read by users. Further, users are likely to be deterred from reading the manual because of the imposing size of the manual.
Graphical calculators are very popular and effective educational aides. School students using graphical calculators can easily visualize complex functions; however, the complexity and cost of currently available graphical calculators deters many students and schools from making a purchase. Purchasers are dissuaded by the size of the manual, multiple modes of operation, and the number of keys and key combinations required for inputting expressions.
Prior hand-held calculators of which the inventor is aware, enable a user to input mathematic expressions for display on a display in a graphical representation. For example, FIG. 8 depicts a graphical representation of the mathematical expression F(x)=sin(x) in a Cartesian coordinate system. Prior approaches for calculators receiving a mathematic expression for graphing include a graphing mode and designation of a graphing key.
Using a graphing mode and designating a graphing key both require a user to manipulate a designated key on the calculator thereby providing input to the calculator indicating that the subsequently entered expression is to be evaluated and a graphical representation thereof displayed. Disadvantageously, the user is required to learn and memorize an additional calculator mode and corresponding activation key, and manipulate additional keys for expression entry. Problematically, the user is more likely to mis-key either the designated graphing mode key or the expression and, at a minimum, additional keystrokes are required to command the calculator to display the graph. Additional keystrokes necessitates more complexity, more time for input, and increased chance of an input error and frustration for the user.
Further disadvantageously, the use of a designated graphing key is expensive in terms of cost and keyboard area for implementation. Additionally, the increased calculator complexity requires a corresponding increase in the size of the user manual needed to describe operation of the calculator to the user.
There is a need in the art for a method of and apparatus for an improved graphical calculator having a user interface for graphing expressions.